The Jacobi symbol is a generalization of the Legendre symbol (a/n) when n is not prime. Let
| n=p1α 1⋯ pkα k | 
be the prime factorization of n. The Jacobi symbol of a is defined by:
| ⎛ ⎜ ⎜ ⎝ | 
 | ⎞ ⎟ ⎟ ⎠ | = | ⎛ ⎜ ⎜ ⎝ | 
 | ⎞ ⎟ ⎟ ⎠ | 
 | … | ⎛ ⎜ ⎜ ⎝ | 
 | ⎞ ⎟ ⎟ ⎠ | 
 | 
Where the left hand side is the Jacobi symbol and the right hand side contains Legendre symbols. The jacobi_symbol command computes the Jacobi symbol.
| jacobi_symbol(25,12) | 
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| jacobi_symbol(35,12) | 
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| jacobi_symbol(33,12) | 
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